In one of the steepest budget cuts he’s ordered in recent years, Mayor Bloomberg yesterday demanded spending slashes of 4 percent in fiscal year 2010 — and an eye-popping 8 percent the next year — for nearly all city agencies.

The combined cuts — which are aimed at saving $1.75 billion for the next budget year, July 1, 2010 through June 2011 — are meant to plug a nearly $5 billion projected gap for the 2011 budget year.

The cuts are the deepest Bloomberg has imposed since the dark fiscal days right after the Sept. 11, 2001, attacks.

Agency heads have until Dec. 3 to produce the lists of cuts, which the City Council must vote on in January.

The fiscal-year 2011 budget is projected to be more than $66 billion without these cuts, but only $24 billion of that total is subject to the mayor’s budget ax.

He would not rule out the possibility of layoffs to the city’s roughly 310,000-member workforce, noting that $36 billion of the current $59.5 billion budget is spent on municipal salaries, including pensions and health benefits.

“So whether it’s attrition or layoffs, some sort of personnel savings is going to be necessary in order to close the $5 billion deficit,” Skyler said.

“It is hard to balance a budget of that size without dealing with the size of the city’s workforce. You can’t rule out anything.”

The Department of Education and four uniformed agencies — Police, Fire, Sanitation and Correction, which make up about 75 percent of discretionary spending — got some reprieve from the mayor’s budget ax.

Bloomberg ordered Education to cut 1.5 percent this year and 4 percent in 2011. The uniformed agencies have to reduce their budgets by 2 percent this year and 4 percent next year.

“Eight percent certainly is big,” remarked Charles Brecher, of the Citizens Budget Commission. “In some ways, it’s reassuring that they’re at least, at the city level, facing up to the magnitude of the problem we have. We didn’t have this discussion during the [mayoral] campaign.”

Despite the cuts, Skyler also did not rule out the possibility that the teachers union, which is negotiating a new contract, could see 4 percent raises for each of the next two years, following the pattern set by other municipal labor deals.

Bloomberg is banking on $200 million in savings from the creation of a new pension tier for municipal employees, but it is unclear whether it has the support it needs in Albany.

The mayor is also negotiating with union leaders in the city to require employees to contribute 10 percent to their health-insurance plans, which would save $360 million in fiscal 2011, spokesman Marc La Vorgna said.